After winning their opening seven games of the season under new coach Niko Kovac, the Bundesliga champions had picked up just one point in their last two games against Augsburg and Hertha Berlin before the Dutch side's visit to the Allianz Arena.
They looked like they would get back on track when Mats Hummels' fourth-minute header put them ahead, but Erik ten Hag's youthful side bounced back in style, levelling midway through the half thanks to Noussair Mazraoui's fine strike.
Substitute James Rodriguez came closest to finding an undeserved winner for Bayern in the second period, while Donny van de Beek will be left to rue a golden opportunity 20 minutes from time for Ajax when he fired wide with only Manuel Neuer to beat.
Andre Onana kept out Arjen Robben's whipped effort in the opening exchanges, but was helpless to stop Hummels' unmarked header from the Dutchman's precise cross shortly afterwards.
Ajax responded well to that early setback, though, with Dusan Tadic firing over from eight yards and Hakim Ziyech testing Neuer from distance in quick succession.
Their renewed confidence paid dividends in the 22nd minute when Mazraoui played a smart one-two with Tadic before drilling past Neuer from 12 yards for his first Ajax goal.
The visitors were dominant for the remainder of the opening period and were only denied a half-time lead when Neuer parried over Ziyech's powerful 30-yard drive.
Tadic wasted another wonderful opportunity moments after the restart, scuffing a close-range effort from David Neres' cross, while Nicolas Tagliafico's low drive was kept out by Neuer.
Hummels was denied what looked a clear penalty after being clattered by Onana just before the hour mark before Van de Beek steered agonisingly wide.
Onana did wonderfully to tip James' scuffed effort wide late on, while Ajax almost secured the win their performance deserved in stoppage time, but Neuer tipped Lasse Schone's fizzing free-kick onto the crossbar.
What does it mean: Bayern with work to do
The Bundesliga champions were expected to qualify from Group E at a canter, but they are not going to have it all their own way. Benfica's win over AEK Athens puts them a point behind the Bavarian giants and Ajax, who both have four. Kovac's side are going to need a significant improvement if they are to make the knockout stages.
De Ligt lights up Allianz Arena
It is hard to believe the 19-year-old was making his Champions League debut. He was imperious at the heart of Ajax's defence and scarcely gave Robert Lewandowski a kick.
Lewandowski looked lost
The Polish striker was praised by Kovac recently for his response after a proposed move to Real Madrid failed to materialise. He looked a shadow of his former self against Ajax, though, posing no goal threat at all in what was a limp display.
Key Opta facts
- Bayern Munich failed to win three consecutive home games in the Champions League for the first time since November 2009.
- Ajax are winless in 11 away games in the Champions League (D5 L6), equalling their worst ever run in the competition, set back in September 2005.
- Mats Hummels scored his second Champions League goal for Bayern Munich – both have been headers assisted by Arjen Robben.
- Hummels' opener for Bayern Munich (3:42) was the second quickest that Ajax have ever conceded in the Champions League, slower only than Freddie Ljungberg's effort for Arsenal in September 2005 (1:19).
Bayern will be hoping to return to winning ways in the Bundesliga on Saturday when Borussia Monchengladbach visit the Allianz Arena, while Ajax host AZ in the Eredivisie the following day.